In Agatha Christie's "The Murder of Roger Ackroyd", the following passage appears:

Ackroyd has always interested me by being a man more impossibly like a country squire than any country squire could really be. He reminds one of the red-faced sportsmen who always appeared early in the first act of an old-fashioned musical comedy, the setting being the village green. They usually sang a song about going up to London. Nowadays we have revues, and the country squire has died out of musical fashion.

Now, presumably for a contemporary reader at the time (the book was published in 1926) this would be a very illuminating description. However, as a reader from 90 years in the future, I'm completely at a loss. What was the role of a "country squire", what did they generally do, what were the intended stereotypes that one might be? What was the style of an "old-fashioned musical comedy" and are there examples with a country squire I could look up?

My websearches for "Country Squire" have mostly things named after the phrase, such as the motorcar from 1950 and plenty of hostelry.

This is not a question about historical events. A country squire is a rich guy that lives a retired life in a rural area. That Agatha Christie sold 100 million books writing this tripe annoys me.
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Tyler DurdenAug 19 '14 at 16:03

Since the question was originated from a novel, I'll comment from a novel. In Jane Austen's Pride and Prejudice, Mr. Bennett, the beleaguered Patron of the family of unwed sisters, was a "Country Squire" and even Mr. Darcy would be termed such.
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CGCampbellAug 19 '14 at 21:55

Lord Denning, in Corpus Christi College Oxford v Gloucestershire
County Council [1983] QB 360, described the manor thus:

“In mediæval times the manor was the nucleus of English rural life. It
was an administrative unit of an extensive area of land. The whole of
it was owned originally by the lord of the manor. He lived in the big
house called the manor house. Attached to it were many acres of
grassland and woodlands called the park. These were the “demesne
lands” which were for the personal use of the lord of the manor.
Dotted all round were the enclosed homes and land occupied by the
“tenants of the manor”.

By 1926 I imagine the title-holder would have few or no special powers, but people would have been familiar with the historical feudal origins.

In the 18th and 19th-centuries, a "squire" could also be a designated landowner (possibly of renown) who served as a private legal entity in the local court system. He was an "arm" of the Judge or Magistrate himself. Source: http://www.bunker8.pwp.blueyonder.co.uk/history/36804.htm - “Law, Ideology & the Gallows in 18th & 19th Century England." I have a G.G. Grandfather who was always called "Squire" Hugh (1801-1870) - who migrated here to Appalachia - who served on the county court as it was just getting established. Some "squires" meted out punishment in trials, some were paid fees. They were called "harlan" in earlier centuries (see Crooked Talk: 500 Years of the Language of Crime by Jonathon Greeen - excerpts are available at books.google).